Discontinuous Galerkin Methods for Morphodynamic Modelling

TASSI PA; RHEBERGEN S; VIONNET CA; BOKHOVE O

Venice, Italy

Congreso; ECCOMAS 2008 - 5th European Congress on Computational Methods in Applied Sciences and Engineeering; 2008

International Association for Computational Mechanics (IACM), European Community on Computational Methods in Applied Sciences (ECCOMAS), Faculty of Engineering, University of Padua, Italy

The interaction between sediment transport and water flow plays an important role in many river and coastal engineering applications. In recent years, the improved understanding of physical processes involved in the study of river hydraulics has led to the development of physical-mathematical formulations to explain the natural phenomena and to forecast changes due to, for example, human interference. Nevertheless, accurate representation of morphodynamic processes and the ability to propagate changes in the riverbed over a wide range of space and time scales make the design and implementation of appropriate numerical schemes challenging. Prediction of changes of the bed in natural channels can be analyzed by coupling a hydrodynamic flow solver which acts as a sediment driving force and a bed evolution model which accounts for sediment flux and bathymetry changes. Such a modelling system is often referred to as a morphodynamic model. The morphodynamic model emerges as a mixed hyperbolic–parabolic system of partial differential equations (PDE’s). It is based on a depth–average over the water column resulting in shallow water theory augmented by a flow resistance term, together with a depth–averaged conservation law expressing continuity of sediment. A phenomenological sediment transport function relates the rate of sediment transport to the local mean fluid velocity. Here, we consider that sediment particles are carried along via bedload transport. There are special difficulties associated with solving hyperbolic equations, including the propagation of sediment bores or discontinuous steps in the bedform, and a good numerical implementation must overcome these problems. In this work, we use a novel space and space–time discontinuous Galerkin finite element method (DGFEM). The use of DGFEM methods for these problems is also of interest because it is local and can thus deal efficiently with: (i) the improvement of the order of accuracy, thus allowing efficient p-adaptivity; (ii) the refinement of the grid, without taking into account the continuity restrictions typical of conforming finite element methods, thus allowing efficient h-adaptivity; and, (iii) performing parallel computations.